Question: Simplify the following expression: $ n = \dfrac{-1}{5} + \dfrac{-10}{z + 9} $
Explanation: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{z + 9}{z + 9}$ $ \dfrac{-1}{5} \times \dfrac{z + 9}{z + 9} = \dfrac{-z - 9}{5z + 45} $ Multiply the second expression by $\dfrac{5}{5}$ $ \dfrac{-10}{z + 9} \times \dfrac{5}{5} = \dfrac{-50}{5z + 45} $ Therefore $ n = \dfrac{-z - 9}{5z + 45} + \dfrac{-50}{5z + 45} $ Now the expressions have the same denominator we can simply add the numerators: $n = \dfrac{-z - 9 - 50}{5z + 45} $ $n = \dfrac{-z - 59}{5z + 45}$